The fundamental
principles of geochemical cycling were stumbled upon by John Joly
in the latter 1800's when he attempted to determine the age of
the Earth by estimating the time required for "salt" to
accumulate in the oceans. To do this, Joly simply calculated the
total mass of salt in the oceans (by multiplying the
concentration of salt in seawater by the volume of the oceans)
and dividing this mass by the annual flux of salt to the oceans
from rivers. While this method is computationally correct, it
does not yield the age of the Earth, but rather the RESIDENCE
TIME (i.e. the average length of time "salt" resides in
the oceanic reservoir).

1. Let's reenact
Joly's computation to see how much fun it might be! To do this,
you need some basic data about the ocean and rivers.

Calculate the total volume of water
in the ocean. Assume the average depth is
3700 m and the area of the ocean is 360 x 106
km2. What is your answer in km3?
What is your answer in liters?

Calculate the total mass of sodium
in the ocean. Assume the average
concentration of sodium in seawater is 10,500
mg/L. What is this mass in grams?

Use the table below to calculate the
annual flux of water from rivers to the
ocean.

RIVER

ANNUAL
Q (km3)

% OF TOTAL

CUMULATIVE %

AMAZON

6300

42.4

42.4

CONGO (ZAIRE)

1250

8.4

50.8

ORINOCO

1100

7.4

58.2

YANGTZE

900

6.1

64.2

BRAHMAPUTRA

603

4.1

68.3

MISSISSIPPI

580

3.9

72.2

YENISEI

560

3.8

76.0

LENA

514

3.5

79.4

MEKONG

470

3.2

82.6

LA PLATA

470

3.2

85.7

GANGES

450

3.0

88.8

IRRAWADDY

428

2.9

91.6

ST. LAWRENCE

447

3.0

94.7

MACKENZIE

306

2.1

96.7

COLUMBIA

251

1.7

98.4

INDUS

238

1.6

100.0

What is the value of the
total annual flux of water from rivers to the
ocean?

Assume water entering
the ocean from rivers has an average sodium
concentration of 5.15 mg/L

What is the total mass
of sodium delivered to the ocean each year by
rivers (i.e. the sodium flux)?

What is the residence
time of sodium in the ocean?

Calculate the discharge
in cubic feet per second for the rivers
above.

3. "The Magnesium Problem" was
resolved in 1977, following the discovery of hydrothermal vents
along a portion of the mid-ocean ridge system near the Galapagos
Islands. Here it was discovered that the Mg flux into rocks near
the ridge crest was approximately equal to the annual flux of Mg
delivered to the ocean via rivers. Using the calculated Mg flux
into ocean ridges, the residence time of Mg in the ocean was
determined to be approximately 10 million years. Put another way,
a volume of water equivalent to the entire volume of the ocean
was cycled through the world mid-ocean ridge system every 10
million years! Using the information below, calculate the volume
of water (in cubic feet per second) which must be processed
through each meter length of the mid-ocean ridge every minute to
accomplish this task.

volume of ocean = 1.332 x
109 km3 = how many cubic
feet is this?

length of mid-ocean ridge
system = 42,000 miles = 67,580 km

Your calculated answer may seem
extraordinary to you. This is because we are using a somewhat
misleading parameter (each meter length of ridge). A better
figure would be to estimate the flow through each square meter of
ridge. For the sake of argument, let's assume that hydrothermal
activity is restricted to a region extending 20 km on either side
of the ridge crest. Now calculate the required seawater flow
through ridge rocks to process the ocean volume in 10 million
years.